I just want to double check.
Since In My Sights says when the movement is declared, I take it to mean the shot happens before the movement.
Yes; it also says "Valentine can make a free Ranged Attack against it before it moves
As for the unlimited range, the penalty for long distance still applies to her basic ranged attack, right?
I see no reason why the range on the Reactive Attack would be unlimited. It should still have her usual 16" maximum range. From my reading, the only thing that's unlimited is the range at which "In My Sights" can be tagged on an enemy.
As for why it only limits the declaration to LoS but doesn't list a range, I suspect it's because Valentine might declare IMS, then move closer to an enemy to put them inside her range, and then shoot them for free when they move. Also, a few characters can take two Movement Actions in the one Turn, so someone might move into range and then move again.